Man is has been able to discover some Laws of Nature.  What of the Laws of the Spirit?  Plato said "God ever geometrizes."  Mathematics may be related to archetypes of the Collective Unconscious.  And what is the Harmony of the Spheres?



Sacred Geometry

Beautiful cross section of a Nautilus seashell. nautilus
A Fibonacci spiral drawn with squares with sides according to the sequence 1, 2, 3, 5, 8... spiral

As we look out on the world we can see amazing shapes and structures.  Man has sought to duplicate some of this beauty and also to unravel the mystery often through mathematics.  The triangle and circle are the simplest sacred symbols.
Fibonacci was an Italian mathematician of the Middles Ages (around 1200 A.D.).  He grew up in North Africa and learned Arabic mathematics.  Algebra, for example, is an Arabic term.  Fibonacci developed a very interesting sequence that shows up surprisingly in nature as can be seen in the spiral structure of the Nautilus.
The simple sequence is: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 ...
Starting with 1, the next number is obtained by adding the two numbers before. 
The ratio of two consecutive numbers, for example, 34/21, approach a value of 1.618034, called Phi or the Golden Mean.  The Nautilus spiral grows by Phi every turn.  Pine cones and sunflowers grow in this pattern.  This appears to a very efficient use of space and proportion in nature.     


pythagoras Pythagoras Experimenting With Sound, woodcut, 1492

Pythagorus, the famous Greek mathematician and philosopher of the 5th century B.C., developed musical scales in terms of harmonic ratios. 
   The Pythagorean Brotherhood, a Mystery School, taught about sacred geometry, harmony and union with the divine.  In medieval times, Pythagorus was rediscovered, and certain numbers and proportions were considered proof of God’s creation.  Pythagoras  hypothesized the planets and sun and moon orbits were related in ratios and connected to all things by musical vibrations.  He termed this the "music or harmony of the spheres".  Astronomers Tycho Brahe and Johannes Kepler did prove that the planets moved in elliptical orbits about the Sun in certain ratios.  This led to the overthrow of the  "earth centered" theory of the universe and helped begin the scientific revolution.

Yin and Yang

The Yin - Yang Symbol

This represents opposites and unity in perfect harmony.

Yin         Yang

dark          light

matter        spirit

earth         heaven



Sometimes nature seems to be very chaotic such as in storms and volcanoes.  But beneath that chaos, there is order and law.  Temperature, pressure and concentration differences produce the patterns.  Hurricanes, in essence, are determined by heat energy and air pressure differences. 
Snowflakes, ferns, trees, crystals and even rivers grow and spread out in patterns called fractals that can be described with mathematical equations.  A fractal is a repeating geometric pattern with variable dimensions determined by a set rule or equation.    Benoit B. Mandelbrot, a Polish and French mathematician introduced this term in 1975.

A computer generated Mandelbrot - type fractal image. mandelbrot

God the Geometer

13th Century

God shown with a compass.

Looks like fractals.


The Next Reformation is interested in the Laws of Nature and the Laws of the Spirit.

Now consider the Collective Unconscious ~